The sequence provided is $19, 16, 13, 10, \dots$. This is an arithmetic sequence because the difference between consecutive terms is constant.

Let's find the common difference, $d$, of the sequence: $d = 16 - 19 = -3$

The general formula for the $n$-th term of an arithmetic sequence is: $A_n = A_1 + (n-1) \cdot d$ where:

• $A_1$ is the first term,
• $d$ is the common difference, and
• $n$ is the term number.

Given that $A_1 = 19$, $d = -3$, and $n = 19$, we can substitute these values into the formula to find $A_{19}$:

$A_{19} = 19 + (19 - 1) \cdot (-3)$ $A_{19} = 19 + 18 \cdot (-3)$ $A_{19} = 19 - 54$ $A_{19} = -35$

Thus, the 19th term of the sequence is $A_{19} = -35$.

Would you like any more details on this solution? Here are some additional related questions:

1. What is the formula for the sum of the first $n$ terms of an arithmetic sequence?
2. How can you find the 50th term of the same sequence?
3. What is the common difference and how does it affect the sequence?
4. How would the sequence change if the common difference was positive?
5. How can you determine if a sequence is arithmetic just by looking at a few terms?

Tip: Always check if the difference between terms is constant to confirm that a sequence is arithmetic.